Q10. - Algebra 1

Question

GAMES Fifty girls and 75 boys attend a sports club. For a game, boys and girls are going to split into groups. The number in each group has to be the same. How large can the groups be?

Step-by-Step Solution

Answer

Each group will have $25$ people.

Step 1. Define greatest common factor.

Greatest common factor is the product of common prime factors of two or more whole numbers. It is a greatest number that is factor of both numbers.

Step 2. Factor each number.

To find how large a group can be, find GCF of the numbers.

$\begin{array}{c}50=2\cdot 5\cdot 5\\ 75=3\cdot 5\cdot 5\end{array}$

Step 3. Find the greatest common factor.

Combine common prime factors to find greatest common factor.

$5\cdot 5=25$

Therefore, each group will have 25 people.